一种构造可积Hamilton系统的新方法

A New Method for the Construction of Integrable Hamiltonian Systems

建议了一种新的构造可积Ｈａｍｉｌｔｏｎ系统的方法．对于给定的Ｐｏｉｓｓｏｎ流形，本文利用Ｄｉｒａｃ－Ｐｏｉｓｓｏｎ结构构造其上的新Ｐｏｉｓｓｏｎ括号［１］，进而获得了新的可积Ｈａｍｉｌｔｏｎ系统．构造的Ｐｏｉｓｓｏｎ括号一般是非线的；并且这种方法也不同于通常的方法［２～４］。本文还给出了两个实例．

A new method for the construction of integrable Hamiltonian system is proposed. For a given Poisson manifold, the present paper constructs new Poisson brackets on it by making use of the Dirac Poisson structure([11 ), and obtains further new integrable Hamiltonian systems. The constructed Poisson bracket is usual non-linear, and this new method is also different from usual ones ([24] ). Two examples are given.